Search results for " Geometry"
showing 10 items of 2294 documents
Lie Algebras Generated by Extremal Elements
1999
We study Lie algebras generated by extremal elements (i.e., elements spanning inner ideals of L) over a field of characteristic distinct from 2. We prove that any Lie algebra generated by a finite number of extremal elements is finite dimensional. The minimal number of extremal generators for the Lie algebras of type An, Bn (n>2), Cn (n>1), Dn (n>3), En (n=6,7,8), F4 and G2 are shown to be n+1, n+1, 2n, n, 5, 5, and 4 in the respective cases. These results are related to group theoretic ones for the corresponding Chevalley groups.
Synthesis, characterization, and cytotoxic activity of copper(II) and platinum(II) complexes of 2-benzoylpyrrole and X-ray structure of bis[2-benzoyl…
2004
Copper(II) and platinum(II) complexes of 2-benzoylpyrrole (2-BZPH) were synthesized and characterized with IR, 1 H and 1 3 C NMR spectroscopies and coordination geometry with ligands arranged in transoid fashion. The crystal structure of [Cu I I (2-BZP) 2 ] was determined by X-ray diffraction. Death of complex treated Jurkat cells was measured by flow cytometry. The bis-chelate complexes [Cu I I (2-BZP) 2 ] and [Pt I I (2-BZP) 2 ] adopt square-planar coordination geometry with ligands, arranged in transoid fashion. Concentrations of 1-10 μM Platinum(II) complexes reduced cell survival from 100% to 20%, in contrast to the copper(II) complex which caused no cell death at a concentration of 10…
Preparation and structural characterization of organotin(IV) complexes with ligands containing a hetero {N} atom and a hydroxy group or hydroxy and c…
2005
AbstractTwenty-two n-butyltin(IV) and t-butyltin(IV) complexes of ligands containing an –OH (–C@O) group or –OH and –COOHgroups and an aromatic {N} donor atom were prepared by metathetical reactions. On the basis of the FT-IR and Mo¨ssbauer spec-troscopic data, molecular structures were assigned to these compounds. The binding sites of the ligands were identified by means ofFT-IR spectroscopic measurements, and it was found that in most cases the organotin(IV) moiety reacts with the phenolic form ofthese ligands. In the complexes with –OH and –COOH functions, the –COOH group is coordinated to the organotin(IV) centres in amonodentate manner. The 119 Sn Mo¨ssbauer and the FT-IR studies suppor…
Geometric rough paths on infinite dimensional spaces
2022
Similar to ordinary differential equations, rough paths and rough differential equations can be formulated in a Banach space setting. For $\alpha\in (1/3,1/2)$, we give criteria for when we can approximate Banach space-valued weakly geometric $\alpha$-rough paths by signatures of curves of bounded variation, given some tuning of the H\"older parameter. We show that these criteria are satisfied for weakly geometric rough paths on Hilbert spaces. As an application, we obtain Wong-Zakai type result for function space valued martingales using the notion of (unbounded) rough drivers.
Integrability of orthogonal projections, and applications to Furstenberg sets
2022
Let $\mathcal{G}(d,n)$ be the Grassmannian manifold of $n$-dimensional subspaces of $\mathbb{R}^{d}$, and let $\pi_{V} \colon \mathbb{R}^{d} \to V$ be the orthogonal projection. We prove that if $\mu$ is a compactly supported Radon measure on $\mathbb{R}^{d}$ satisfying the $s$-dimensional Frostman condition $\mu(B(x,r)) \leq Cr^{s}$ for all $x \in \mathbb{R}^{d}$ and $r > 0$, then $$\int_{\mathcal{G}(d,n)} \|\pi_{V}\mu\|_{L^{p}(V)}^{p} \, d\gamma_{d,n}(V) \tfrac{1}{2}$ and $t \geq 1 + \epsilon$ for a small absolute constant $\epsilon > 0$. We also prove a higher dimensional analogue of this estimate for codimension-1 Furstenberg sets in $\mathbb{R}^{d}$. As another corollary of our method,…
Isometric embeddings of snowflakes into finite-dimensional Banach spaces
2016
We consider a general notion of snowflake of a metric space by composing the distance by a nontrivial concave function. We prove that a snowflake of a metric space $X$ isometrically embeds into some finite-dimensional normed space if and only if $X$ is finite. In the case of power functions we give a uniform bound on the cardinality of $X$ depending only on the power exponent and the dimension of the vector space.
Duality of moduli in regular toroidal metric spaces
2020
We generalize a result of Freedman and He [4, Theorem 2.5], concerning the duality of moduli and capacities in solid tori, to sufficiently regular metric spaces. This is a continuation of the work of the author and Rajala [12] on the corresponding duality in condensers. peerReviewed
Semantic-based Technique for the Automation the 3D Reconstruction Process
2010
Pages: 191 to 198, ISBN: 978-1-61208-104-5; International audience; The reconstruction of 3D objects based on point clouds data presents a major task in many application field since it consumes time and require human interactions to yield a promising result. Robust and quick methods for complete object extraction or identification are still an ongoing research topic and suffer from the complex structure of the data, which cannot be sufficiently modeled by purely numerical strategies. Our work aims at defining a new way of automatically and intelligently processing of 3D point clouds from a 3D laser scanner. This processing is based on the combination of 3D processing technologies and Semant…
Strong BV-extension and W1,1-extension domains
2021
We show that a bounded domain in a Euclidean space is a $W^{1,1}$-extension domain if and only if it is a strong $BV$-extension domain. In the planar case, bounded and strong $BV$-extension domains are shown to be exactly those $BV$-extension domains for which the set $\partial\Omega \setminus \bigcup_{i} \overline{\Omega}_i$ is purely $1$-unrectifiable, where $\Omega_i$ are the open connected components of $\mathbb{R}^2\setminus\overline{\Omega}$.
Ahlfors-regular distances on the Heisenberg group without biLipschitz pieces
2015
We show that the Heisenberg group is not minimal in looking down. This answers Problem 11.15 in `Fractured fractals and broken dreams' by David and Semmes, or equivalently, Question 22 and hence also Question 24 in `Thirty-three yes or no questions about mappings, measures, and metrics' by Heinonen and Semmes. The non-minimality of the Heisenberg group is shown by giving an example of an Ahlfors $4$-regular metric space $X$ having big pieces of itself such that no Lipschitz map from a subset of $X$ to the Heisenberg group has image with positive measure, and by providing a Lipschitz map from the Heisenberg group to the space $X$ having as image the whole $X$. As part of proving the above re…